Suppose the production process tor running shoes is given by q = iDKL where q is the number of pairs of running shoes produced, K is the number of machine hours of sewing and, L is the number of personhours of labor. 1. Derive the costminimizing demands for K and L as a function of output {q}, wage rates {w}, and rental rate on machines {r}. 2. Write the total cost function for running shoes as a function of q. r, and w. 3. Suppose the producer wants to make 2000 pairs of running shoes. If the current wage rate is $25 per hour and the rental rate on machines is $50 per hour, find the costminimizing combination of inputs to make the desired quantity. 4. What is the total cost of production tor 2000 units